When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the nuclear spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. Usually the nuclear spins are comprised of hydrogen atoms, but other NMR active nuclei are occasionally used. A net magnetic moment, Mz, is produced in the direction of the polarizing field, but the randomly oriented magnetic components in the perpendicular, or transverse, plane (x-y plane) cancel one another. If, however, the substance, or tissue, is subjected to a magnetic field (excitation field, B1; also referred to as the radiofrequency (“RF”) field) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped” into the x-y plane to produce a net transverse magnetic moment, Mt, which is rotating, or spinning, in the x-y plane at the Larmor frequency. The practical value of this phenomenon resides in the signal which is emitted by the excited spins after the excitation field B1 is terminated. There are a wide variety of measurement sequences in which this nuclear magnetic resonance (“NMR”) phenomenon is exploited.
When utilizing these signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged experiences a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The emitted MR signals are detected using a receiver coil. The MRI signals are then digitized and processed to reconstruct the image using one of many well-known reconstruction techniques.
Parallel imaging techniques use spatial information from arrays of RF receiver coils to substitute for the encoding that would otherwise have to be obtained in a sequential fashion using RF pulses and field gradients (such as phase and frequency encoding). Each of the spatially independent receiver coils of the array carries certain spatial information and has a different sensitivity profile. This information is utilized in order to achieve a complete location encoding of the received MR signals by a combination of the simultaneously acquired data received from the separate coils. Specifically, parallel imaging techniques undersample k-space by reducing the number of acquired phase-encoded k-space sampling lines while keeping the maximal extent covered in k-space fixed. The combination of the separate MR signals produced by the separate receiver coils enables a reduction of the acquisition time required for an image (in comparison to conventional k-space data acquisition) by a factor that in the most favorable case equals the number of the receiver coils. Thus the use of multiple receiver coils acts to multiply imaging speed, without increasing gradient switching rates or RF power.
The signal processing technique referred to as compressed sensing (“CS”) facilitates reconstruction of signals from an incomplete Fourier representation, provided that certain conditions are met. This technique is capable of allowing the acceleration of MRI by collecting less data than conventionally required, thereby reducing the scan time. One condition that allows successful CS recovery is that the signal should be compactly represented under a mathematical transform. Another such condition is that the Fourier representation of the signal should be sampled so that the aliasing artifacts under this transform are incoherent. Still another condition is that a non-linear signal processing algorithm should be applied to enforce a compact representation while preserving the acquired data. Non-linear iterative CS reconstructions using sparsifying transforms are finding utility in various applications, but require a change in undersampling patterns to ensure that the incoherency condition is met. Unfortunately, most clinically-available uniform undersampling patterns yield aliasing artifacts that are not incoherent.
As techniques such as parallel imaging and compressed sensing are used to push the speed and complexity of MR imaging techniques, other limitations, such as noise, raise in prevalence.